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Recent photometric studies have shown that early-type galaxies at fixedstellar mass were smaller and denser at earlier times. In this paper we assessthat finding by deriving the dynamical mass of such a compact quiescent galaxyat z=1.8. We have obtained a high-quality spectrum with full UV-NIR wavelengthcoverage of galaxy NMBS-C7447 using X-Shooter on the VLT. We determined avelocity dispersion of 294 +- 51 km/s. Given this velocity dispersion and theeffective radius of 1.64 +- 0.15 kpc (as determined from HST-WFC3 F160Wobservations) we derive a dynamical mass of 1.7 +- 0.5 x 10^11 Msun. Comparisonof the full spectrum with stellar population synthesis models indicates thatNMBS-C774 has a relatively young stellar population (0.40 Gyr) with little orno star formation and a stellar mass of ~1.5 x 10^11 Msun. The dynamical andphotometric stellar mass are in good agreement. Thus, our study supports theconclusion that the mass densities of quiescent galaxies were indeed higher atearlier times, and this earlier result is not caused by systematic measurementerrors. By combining available spectroscopic measurements at differentredshifts, we find that the velocity dispersion at fixed dynamical mass was afactor of ~1.8 higher at z=1.8 compared to z=0. Finally, we show that theapparent discrepancies between the few available velocity dispersionmeasurements at z>1.5 are consistent with the intrinsic scatter of themass-size relation.

the astrophysical journal. letters

The stellar velocity dispersion of a compact massive galaxy at z=1.80  using X-Shooter: confirmation of the evolution in the mass-size and  mass-dispersion relations